OverviewMost physically interesting problems are governed by ordinary, or partial differential equations. It is examples of such equations that provide the motivation for the material covered in this module, and there is a strong emphasis on physical applications throughout. The aim of the module is to provide a firm grounding in mathematical methods: both for solving differential equations and, through the study of special functions and asymptotic analysis, to determine the properties of solutions. The following topics will be covered: Ordinary differential equations: method of Frobenius, general linear second order differential equation. Special functions: Bessel, Legendre, Hermite, Laguerre and Chebyshev functions, orthogonal functions, gamma function, applications of special functions. Partial differential equations; linear second order partial differential equations; Laplace equation, diffusion equation, wave equation, Schrödingers equation; Method of separation of variables. Fourier series: application to the solution of partial differential equations. Fourier Transforms: Basic properties and Parsevals theorem.
This module appears in:
Contact hours: 34 lectures, 10 workshops.
Total study hours, including private study: 150.
This is not available as a wild module.
Method of assessment
30% coursework including class tests; 70% final exam.
M Boas Mathematical Methods in the Physical Sciences (3rd ed., Wiley, 2005) ISBN: 978-0-471-36580-8
An ability to solve problems in physics using appropriate mathematical tools.
An ability to present and interpret information graphically.
An ability to make use of appropriate texts, or other learning resources as part of managing their own learning.
Problem-solving skills - in the context of both problems with well-defined solutions and open-ended problems; an ability to formulate problems in precise terms and to identify key issues, and the confidence to try different approaches in order to make progress on challenging problems. Numeracy is subsumed within this area.
Analytical skills associated with the need to pay attention to detail and to develop an ability to manipulate precise and intricate ideas, to construct logical arguments and to use technical language correctly.